Euro zone finance ministers and the International Monetary Fund have agreed to release 49.1 billion euros in aid to Greece by the end of March, with most of that sum flowing immediately, senior EU officials said on Thursday.

"Money will be flowing to Greece as early as next week," Eurogroup Chairman Juncker told a news conference after a meeting of ministers from the single currency bloc. "We are convinced the program is back on a sound track."

A Eurogroup statement said 34.3 billion euros would be paid out in the coming days and the remainder in the first quarter of 2013. Agreement to release the funds hinged on the success of a debt buyback launched by Greece last week, which will enable Athens to retire nearly 20 billion euros in bonds repurchased at a third of their face value from private holders.

Juncker said he was not sure that additional measures would be needed to reach an agreed goal to bring Greece's debt down to 124 percent of gross domestic product (GDP) by 2020, but the bloc stood ready to take new steps if necessary.

The agreement follows the completion of a bond buyback scheme which was hailed as a success by international lenders and was seen as a key stepping stone in getting the next tranche of aid.The scheme was intended to put Greece's debt mountain on a more sustainable footing but is now expected to cut it by less than initially hoped because of higher-than-expected prices to buy back the bonds.

To make up the shortfall, Athens asked its foreign lenders for an extra 1.29 billion euros over the 10 billion euros initially allotted to buy back all the 31.9 billion in bonds tendered in the scheme.

European paymaster Germany and the International Monetary Fund both welcomed the outcome of the buyback, signaling Athens was on its way to getting over 34 billion euros in aid this month to recapitalize its struggling banks.